I've been hearing about Halley's comet for a while now, and I'm just curious as to when and where to see it, and for how long. :)
Halley's comet orbits the sun and its orbit lasts 75 years. The orbit is a long elliptical orbit. For most of those 75 years it is a cold black dot, and frozen solid in the outer solar system. But a short period during that orbit it gets close to the sun. The ice and gas begin to boil of its surface and gets blown back by the solar wind of the sun. It then starts to look like a comet.
The last time Halley's comet was close to the sun was in 1986, and so the next time will be in 2061. You won't be able to see Halley's comet until then.
(image from University of Wisconsin)
I remember 1986, and the comet was visible but hard to see. It was a very dim fuzzy dot, that was just about visible in my binoculars. This is because, unfortunately, the Earth was a long way from the comet. In 2061 Earth will be even further from the comet, however Earth will be better positioned when Halley is closest to the sun, so it should make a good show, and be clearly visible to the naked eye. Comet predictions are hard as much depends on exactly how much water vapour boils off, and this is hard to predict. Comets can have sudden changes in activity.
Moreover, Halley's comet isn't the only comet. There are others that can be as visible as Halley will be in 2061. There are also long period comets that are undiscovered until they come close to the sun. These can be very bright. Comet Hale-Bopp was a "great" comet in 1997 and was visible for many months. Another great comet could come along any time but we can't predict when.